It is called the bell-shaped or Gaussian distribution after its inventor, Gauss although De Moivre also deserves credit. The visual appearance is given below. Property of probability distributions is that area under curve equals one.
A property of a special class of non-negative functions, called probability distributions, is that the area under the curve equals unity.
Alternatively if there is a long tail to the left only we say it is skewed to the left negatively skewed Figure 2 ; or if there is a long tail to the right only we say it is skewed to the right positively skewed Figure 3 :.
If the data is normally distributed the median should be positioned approximately in the centre of the box, both whiskers should have similar length and ideally there should be no outliers Figure 4.
However the variable may be negatively skewed Figure 5 or positively skewed Figure 6 :. If the data is normally distributed the points on a normal Q-Q plot will fall on the straight diagonal line Figure 7. Otherwise, the points will not lie on the straight diagonal line Figures 8 and 9 :. Another version of this plot, the detrended Q-Q plot, is sometimes also analysed; in the detrended plot there should be roughly equal number of points above and below the line, with no obvious trend.
A stem and leaf plot displays the frequency of each value in the data set, organised into 'stems' and 'leaves'. While this plot is less frequently analysed, if you do choose to use it note that it can be interpreted in the same way as a histogram, only rotated on its side. If you would like to practise assessing whether or not data approximates a normal distribution, have a go at the following activity:. If tests for normality indicate that the variable is not normally distributed, you can try transforming the variable so that it conforms more to the normal distribution.
Once the data has been transformed, it should be tested again for normality. It looks like you're using Internet Explorer 11 or older. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. If you continue with this browser, you may see unexpected results. Introduction to statistics: The normal distribution. Introduction Interpreting statistics Data and variable types Descriptive statistics The normal distribution Inferential statistics Glossary Feedback.
Introduction to statistics. Numeracy Skills Fundamentals Algebra Statistics. EndNote Essentials Extras Online. Enter Search Words. The presence of non-normal distributions can be diagnosed in several ways. Visual inspection of a histogram of the nutrient dietary component is a useful but subjective procedure. Most statistical software packages contain a variety of formal statistical tests for the normal distribution hypothesis, such as the Shapiro-Wilk and Kolmogorov-Smirnov tests.
Because many [glossary term:] parametric statistical procedures assume a normal distribution, it may be necessary to normalize the distribution of skewed dietary data through transformation before analysis.
Non-parametric statistical procedures do not have this requirement, and the dietary data can be used without transformation. When an analysis requires variables to be normally distributed, non-normal dietary data can be transformed to obtain data that better approximate normality. Common transformations used for dietary data include log and power e.
The [glossary term:] Box-Cox transformation , introduced by Box and Cox, is a family of transformations that includes the power and log transformations.
To choose the best Box-Cox transformation—the one that best approximates a normal distribution - Box and Cox suggested using the maximum likelihood method.
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